A365120 G.f. A(x) satisfies A(x) = (1 + x / (1 - x*A(x))^2)^2.

1, 2, 5, 18, 70, 294, 1291, 5864, 27314, 129766, 626367, 3063096, 15143562, 75563924, 380062186, 1924840480, 9807649900, 50241194250, 258597717591, 1336730670244, 6936403057274, 36119232561000, 188677598254078, 988464846388710, 5192270327405662

Offset: 0

Author

Seiichi Manyama, Aug 22 2023

Keywords

• nonn

Crossrefs

Cf. A000108, A365121.

Cf. A006013, A365118, A365123.

Cf. A367236.

Programs

PARI

a(n, s=2, t=2) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

Formula

If g.f. satisfies A(x) = (1 + x/(1 - x*A(x))^s)^t, then a(n) = Sum_{k=0..n} binomial(t*(n-k+1),k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A367236. - Seiichi Manyama, Dec 06 2024